Civil Engineering Reference
In-Depth Information
The usable flexural strength of a member,
M
n
, must at least be equal to the calculated
factored moment,
M
u
, caused by the factored loads
M
n
M
u
For writing the beam expressions, reference is made to Figure 3.3. Equating the hori-
zontal forces
C
and
T
and solving for
a
, we obtain
c
ab
A
s
f
y
0.85
f
A
s
f
y
0.85
f
c
b
f
y
d
A
s
a
c
,
where
bd
percentage of tensile steel
0.85
f
Because the reinforcing steel is limited to an amount such that it will yield well be-
fore the concrete reaches its ultimate strength, the value of the nominal moment
M
n
can be
written as
a
2
a
2
M
n
T
d
A
s
f
y
d
and the usable flexural strength is
a
2
M
n
A
s
f
y
d
If we substitute into this expression the value previously obtained for
a
(it was
) and equate
c
f
y
d
/0.85
f
M
n
to
M
u
, we obtain the following expression
1.7
f
y
1
M
n
M
u
A
s
f
y
d
1
c
f
bd
2
, we can solve this expression for
Replacing
A
s
with
bd
and letting
R
n
M
u
/
(the percentage of steel required for a particular
beam) with
the following results:
c
0.85
f
2
R
n
0.85
f
1
1
f
y
c
when rectangular sections are in-
volved, the reader will find Tables A.8 to A.13 in Appendix A of this text to be quite
convenient. (For SI units refer to Tables B.8 and B.9 in Appendix B.) Another way to
Instead of substituting into this equation for
Figure 3.3
